Solution of delay differential equations via a homotopy perturbation method

• Published in: Mathematical and computer modelling Vol. 48; no. 3; pp. 486 - 498
• Main Authors: Shakeri, Fatemeh, Dehghan, Mehdi
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.08.2008; Elsevier Science
• Subjects: Applications in mathematical biology and engineering; Delay differential equations; Exact sciences and technology; Homotopy perturbation method; Mathematical analysis; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis; Numerical analysis. Scientific computation; Ordinary differential equations; Sciences and techniques of general use; Delay differential equations; Homotopy perturbation method; Applications in mathematical biology and engineering; Differential equation; Numerical method; Delay equation; Perturbation method; Numerical analysis; Scientific computation; Applied mathematics; Homotopy; Mathematical model; Computer aided analysis
• ISSN: 0895-7177; 1872-9479
• DOI: 10.1016/j.mcm.2007.09.016

Delay differential equations (denoted as DDE) have a wide range of application in science and engineering. They arise when the rate of change of a time-dependent process in its mathematical modeling is not only determined by its present state but also by a certain past state. Recent studies in such diverse fields as biology, economy, control and electrodynamics have shown that DDEs play an important role in explaining many different phenomena. In particular they turn out to be fundamental when ODE-based models fail. In this research, the solution of a delay differential equation is presented by means of a homotopy perturbation method and then some numerical illustrations are given. These results reveal that the proposed method is very effective and simple to perform.